離散數學
Discrete Mathematics
| 節 | 週一 |
|---|---|
7 15:30–16:20 | 離散數學 MB311（光復） 3 節連堂 |
8 16:30–17:20 | |
9 17:30–18:20 |
* 根據陽明交大上課時間表所列
This course intends to cover four basic areas in the study of computer science: discrete methods, combinatorics, graph theory and finite algebraic structures. We will (1) introduce the topics and techniques of discrete mathematics and combinatorial reasoning; (2) develop the mathematical maturity of the students through the study of an area that is so different from the traditional coverage in calculus and differential equations, and (3) present an adequate survey of topics for the computer science students who will be taking more advanced courses.
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1. Homework and Assignments: 2. Exams and Quizzes: 3. Evaluation and Grading Policy: 4. Pedagogy and other supplementary information (websites, TAs, handouts and/or databases):
Ch. 1: Basic Principles of Counting
- 講授：
- 6
Ch. 3: Set Theory
1. Set and Subsets 2. Set Operations and Laws of Set Theory 3. Counting and Venn Diagrams
- 講授：
- 6
Ch. 4: Properties of Integers 1. Well-Ordering Principle: Mathematical Induction 3
1. Well-Ordering Principle: Mathematical Induction
- 講授：
- 3
Ch. 5: Relations and Functions
Cartesian Products and Relations 2. Plain and One-to-One 3. Onto Functions: Strrling Numbers 4. Pigeonhole Principle 5. Composition and Inverse 6. Computational Complexity
- 講授：
- 6
Ch. 6: Languages: Finite State Machines
Set Theory of Strings 2. Finite State Machines
- 講授：
- 6
Midterm
- 其他：
- 2
Ch. 7: Relations: Second Round
Properties of Relations 2. Computer Recognition: 0-1 Matrices and Directed Graphs 3. Equivalence Relations and Partitions
- 講授：
- 6
Ch. 11: An Introduction to Graph Theory
Ch. 11: An Introduction to Graph Theory 1. Subgraphs, Complements, and Graph Isomorphism 2. Euler Trails and Circuits 3. Hamilton Paths and Cycles 6
- 講授：
- 6
Ch. 12: Trees
Definition and Examples 2. Trees and Binary Trees
- 講授：
- 4
Ch. 13: Optimization and Matching
Dijkstra's Shortest- Path Algorithm 2. Minimal Spanning Trees 3. Complete Binary Tree and Heap
- 講授：
- 7
Final
- 其他：
- 2
| 週次 | 主題 |
|---|---|
| 第 1 週 | Permutations, Combinations |
| 第 2 週 | Catalan Numbers; Set and Subsets, Set Operations |
| 第 3 週 | Laws of Set Theory, Counting and Venn Diagrams |
| 第 4 週 | Well-Ordering Principle: Mathematical Induction |
| 第 5 週 | Cartesian Products and Relations, Plain, One-to-One and Onto Functions |
| 第 6 週 | Pigeonhole Principle, Composition and Inverse, Computational Complexity |
| 第 7 週 | Set Theory of Strings, Finite State Machines |
| 第 8 週 | Finite State Machines |
| 第 9 週 | Midterm Exam. |
| 第 10 週 | Properties of Relations, Computer Recognition: 0-1 Matrices and Directed Graphs |
| 第 11 週 | Equivalence Relations and Partitions |
| 第 12 週 | Subgraphs, Complements, and Graph Isomorphism, |
| 第 13 週 | Graph Isomorphism, Euler Trails and Circuits |
| 第 14 週 | Hamilton Paths and Cycles; Definition and Examples of Trees |
| 第 15 週 | Binary Trees, Dijkstra's Shortest-Path Algorithm |
| 第 16 週 | Minimal Spanning Trees, Complete Binary Tree |
| 第 17 週 | Balanced Binary Tree and Heap |
| 第 18 週 | Final Exam. |
R.P. Grimaldi, Discrete and Combinatorial Mathematics, 5th ED., Addison-Wesley, 2003, Reading, Massachusetts. 新月圖書代理
- 地點
- MB312
- 時間
- 1EF
- 聯絡方式
- sjshyu@gmail.com